Computing with non-orientable defects: Nematics, smectics and natural patterns

Zhang, Chiqun; Acharya, Amit; Newell, Alan C.; Venkataramani, Shankar C.

doi:10.1016/j.physd.2020.132828

Cited by 12 publications

(14 citation statements)

References 38 publications

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“…We expect that the benefits of TADA highlighted in this work will be especially pronounced in the three-dimensional case since disclination lines can only have strength 1/2 (see, e.g., discussion in ref ). The TADA algorithm also generates precisely the geometrical and topological information needed to calibrate and test a recent class of continuum models proposed for line defects in liquid crystals . As such, the TADA algorithm is also a promising technique for supplying nanoscale detail to macroscale models, enabling accurate and efficient multiscale modeling of liquid crystalline materials.…”

Section: Discussionmentioning

confidence: 99%

“…The TADA algorithm also generates precisely the geometrical and topological information needed to calibrate and test a recent class of continuum models proposed for line defects in liquid crystals. 5 As such, the TADA algorithm is also a promising technique for supplying nanoscale detail to macroscale models, enabling accurate and efficient multiscale modeling of liquid crystalline materials.…”

Section: ■ Conclusionmentioning

confidence: 99%

“…The algorithm we develop applies to a director distribution obtained by any means, including through experiments, numerical simulations, or exact solutions of theory of any type. , A recent class of vector field models for topological defects in liquid crystals has been introduced by Zhang et al, making connections with the same class of defects in the elasticity of solids and in convection patterns. Our tool is particularly suited for the validation of such models, which explicitly deal with the layer-like features mentioned above.…”

Section: Introductionmentioning

confidence: 99%

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TADA: The Topology-Accommodating Direction Assignment Algorithm for Liquid Crystals

Saha

Acharya

Wang

2022

J. Chem. Theory Comput.

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Despite the fact that topological defects are a hallmark of liquid crystalline materials, current computational techniques for identifying topological defects in particle-based simulations of these materialswhich rest upon Q-tensor theorydo not leverage topological features of the system. In this work, we describe the topology-accommodating direction assignment (TADA) algorithm, a novel approach for identifying disclination cores in liquid crystalline materials, which is sensitive to topology: this method assigns to each mesogen a unique vector, thereby extending the concept of the liquid crystal director field down to the scale of mesogens. In systems containing disclination cores, TADA identifies line segments along which this assigned vector field is discontinuous, with cores located at the interior termination points of these line segments. The mere presence of defects can be identified by searching far away from them. We validate this approach by comparing its results to those obtained using the scalar order parameter for a variety of liquid crystalline assemblies sourced from molecular-dynamics simulations. We also discuss several benefits of the TADA algorithm over existing approaches for identifying topological defects in liquid crystalline materials.

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Section: Discussionmentioning

confidence: 99%

Section: ■ Conclusionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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TADA: The Topology-Accommodating Direction Assignment Algorithm for Liquid Crystals

Saha

Acharya

Wang

2022

J. Chem. Theory Comput.

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“…One approach to studying point defects in stripe patterns is through a consideration of multi-valued fields [35,41,27]. An alternative is through resolving the physics of the system on a scale at which the defects can be represented by smooth fields [57,56]. We use a third approach by working in the class of SBV functions and allowing for free discontinuities to capture the non-orientability of the underlying patterns.…”

Section: Final Remarksmentioning

confidence: 99%

“…The symmetries of w 0 imply the 'extended' symmetries θ → θ + 2nπ, k → k and θ → −θ, k → −k. One can define topological invariants, based on the monodromy of (θ, k) on traversing a closed circuit in the domain [56]. In particular, any circuit that results in a flip of k encloses a net disclination and the 'elementary' disclinations with degree ± 1 2 are respectively the convex and concave disclinations illustrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

An SBV relaxation of the Cross-Newell energy for modeling stripe patterns and their defects

Venkataramani¹

2021

Preprint

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We investigate stripe patterns formation far from threshold using a combination of topological, analytic and numerical methods. We first give a definition of the mathematical structure of 'multi-valued' phase functions that are needed for describing layered structures or stripe patterns containing defects. This definition yields insight into the appropriate 'gauge-symmetries' of patterns, and leads to the formulation of variational problems, in the class of special functions with bounded variation, to model patterns with defects. We then discuss approaches to discretize and numerically solve these variational problems. These energy minimizing solutions support defects having the same character as seen in experiments.

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Vector Field Models for Nematic Disclinations

et al. 2023

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In this paper, a model for defects in nematic liquid crystals that was introduced in Zhang et al. (Physica D Nonlinear Phenom 417:132828, 2021) is studied. In the literature, the setting of many models for defects is the function space SBV (special functions of bounded variation). However, the model considered herein regularizes the director field to be in a Sobolev space by introducing a second vector field tracking the defect. A relaxation result in the case of fixed parameters is proved along with some partial compactness results as the defect width vanishes.

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Computing with non-orientable defects: Nematics, smectics and natural patterns

Cited by 12 publications

References 38 publications

TADA: The Topology-Accommodating Direction Assignment Algorithm for Liquid Crystals

TADA: The Topology-Accommodating Direction Assignment Algorithm for Liquid Crystals

An SBV relaxation of the Cross-Newell energy for modeling stripe patterns and their defects

Vector Field Models for Nematic Disclinations

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